Estimation and confidence intervals of $$C_{Np}(u,v)$$ C Np ( u, v ) for logistic-exponential distribution with application

Sanku Dey, Mahendra Saha (), M. Z. Anis, Sudhansu S. Maiti and Sumit Kumar
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Sanku Dey: St. Anthony’s College
Mahendra Saha: Central University of Rajasthan
M. Z. Anis: SQC & OR Unit, Indian Statistical Institute
Sudhansu S. Maiti: Visva-Bharati University
Sumit Kumar: Visva-Bharati University

International Journal of System Assurance Engineering and Management, 2023, vol. 14, issue 1, No 30, 446 pages

Abstract: Abstract The process capability index (PCI) has been one of the most useful indicators for evaluating the capability of a manufacturing process. Since PCI is based on sample observations, it is essentially an estimated value. Hence, it is natural to think of a confidence interval (CI) of the PCI. In this paper, bootstrap confidence intervals and highest posterior density (HPD) credible intervals of non-normal PCIs, $$C_{Npmk}$$ C Npmk , $$C_{Npm}$$ C Npm , $$C_{Npk}$$ C Npk and $$C_{Np}$$ C Np are studied through simulation when the underlying distribution is two parameter logistic-exponential (LE). First, maximum likelihood method is used to estimate the model parameters and then three bootstrap confidence intervals (BCIs) are considered for obtaining CIs of non-normal PCIs, $$C_{Npmk}$$ C Npmk , $$C_{Npm}$$ C Npm , $$C_{Npk}$$ C Npk and $$C_{Np}$$ C Np . Next, the Bayesian estimation is studied with respect to symmetric (squared error) loss function using gamma priors for the model parameters. In order to assess the performance of BCIs and HPD credible intervals of $$C_{Npmk}$$ C Npmk , $$C_{Npm}$$ C Npm , $$C_{Npk}$$ C Npk and $$C_{Np}$$ C Np with respect to average width, coverage probabilities and relative coverage, Monte Carlo simulations are conducted. Finally, a real data set, related to weight of the rubber edge of the speaker driver has been analyzed for illustrative purpose.

Keywords: Bayesian estimation; Bootstrap confidence intervals; Logistic exponential distribution; Maximum likelihood estimate; Process capability index (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s13198-023-01870-y

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